Python/algorithms/Graph.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "c9531bac",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>.container{width:100%}</style>\n"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%%HTML\n",
    "<style>.container{width:100%}</style>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "25138dfd",
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import networkx as nx"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "1a17a18b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAgMAAAGbCAYAAABZBpPkAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjkuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8hTgPZAAAACXBIWXMAAA9hAAAPYQGoP6dpAABdyUlEQVR4nO3dd1xV9f8H8Ncd7CVDVBRw4QzT1FAUDGS4E3OPykzLsnLP3ImZpqYlmmUmUm5LzYniCkVNLSMHaoKKguwl4957vn8YfDMFLnAv547X8/H4Pfp6zz3nvPkp97zuZ0oEQRBARERERksqdgFEREQkLoYBIiIiI8cwQEREZOQYBoiIiIwcwwAREZGRYxggIiIycgwDRERERo5hgIiIyMgxDBARERk5hgEiIiIjxzBApCc2btwIiURS8n/m5uZwcXFBcHAwVq1ahezsbLFLJCI9JRe7ACKqmAULFqBBgwYoKirCw4cPcfz4cYwfPx7Lly/Hnj170KpVK7FLJCI9I+FGRUT6YePGjRg5ciTOnz+Pdu3aPXXs2LFj6NWrF5ydnXH16lVYWFiIVCUR6SN2ExAZAH9/f8yePRvx8fHYvHlzyevXrl1D//794eDgAHNzc7Rr1w579ux56tzi7ofTp0/jww8/RM2aNVGjRg288847KCwsREZGBl5//XXY29vD3t4eU6dOxX+/Q+Tm5mLSpElwdXWFmZkZmjZtimXLlj3zPiLSTQwDRAZixIgRAIDDhw8DAGJjY9GhQwdcvXoV06dPx+effw4rKyv07dsXu3fvfub8Dz74AHFxcZg/fz769OmDr7/+GrNnz0bv3r2hVCoRGhqKzp07Y+nSpQgPDy85TxAE9OnTBytWrEC3bt2wfPlyNG3aFFOmTMHEiROr54cnoqoRiEgvfPfddwIA4fz586W+x87OTmjTpo0gCILQtWtXwdPTU8jPzy85rlKpBG9vb8HDw+OZ6wYHBwsqlark9Y4dOwoSiUR49913S15TKBRCvXr1hC5dupS89tNPPwkAhE8++eSpWvr37y9IJBLh5s2blf6Ziah6sGWAyIBYW1sjOzsbaWlpOHbsGAYOHIjs7GykpKQgJSUFqampCA4ORlxcHO7fv//UuaNGjYJEIin5s5eXFwRBwKhRo0pek8lkaNeuHW7fvl3y2v79+yGTyfDhhx8+db1JkyZBEAQcOHBASz8tEWkKZxMQGZCcnBw4Ozvj5s2bEAQBs2fPxuzZs5/73uTkZNStW7fkz25ubk8dt7OzAwC4uro+83p6enrJn+Pj4+Hi4gIbG5un3te8efOS40Sk2xgGiAzEvXv3kJmZicaNG0OlUgEAJk+ejODg4Oe+v3Hjxk/9WSaTPfd9z3td4MBAIoPCMEBkIIoH9QUHB6Nhw4YAABMTEwQEBGj1vu7u7oiMjER2dvZTrQPXrl0rOU5Euo1jBogMwLFjx7Bw4UI0aNAAw4YNg7OzM1555RWsW7cODx48eOb9jx490ti9e/ToAaVSiS+//PKp11esWAGJRILu3btr7F5EpB1sGSDSMwcOHMC1a9egUCiQlJSEY8eO4ciRI3B3d8eePXtgbm4OAPjqq6/QuXNneHp6YvTo0WjYsCGSkpJw5swZ3Lt3D7///rtG6unduzf8/Pwwa9Ys3LlzBy+++CIOHz6Mn3/+GePHj0ejRo00ch8i0h6GASI9M2fOHACAqakpHBwc4OnpiZUrV2LkyJFPNdO3aNECFy5cwPz587Fx40akpqbC2dkZbdq0KbmGJkilUuzZswdz5szB1q1b8d1336F+/fpYunQpJk2apLH7EJH2cDliIiIiI8cxA0REREaOYYCIiMjIMQwQEREZOYYBIiIiI8cwQEREZOTUmlqoUqmQmJgIGxubpzYyISIiIt0lCAKys7Ph4uICqbT07/9qhYHExMRnNishIiIi/XD37l3Uq1ev1ONqhYHihUzu3r0LW1tbzVRGREREWpWVlQVXV9dndhX9L7XCQHHXgK2tLcMAERGRnimvi58DCImIiIwcwwAREZGRYxggIiIycgwDRERERo5hgIiIyMgxDBARERk5hgEiIiIjxzBARERk5BgGiIiIjBzDABERkZFjGCAiIjJyDANERERGjmGAiIjIyDEMEBERGTmGASIiIiPHMEBERGTk5GIXQEREpC9yCxS4k5qLQoUKpnIp6jtawcpM/x+l+v8TEBERaVFcUjYiYhIQdT0ZCWl5EP51TALAzcESfk2dMczLDR61bMQqs0okgiAI5b0pKysLdnZ2yMzMhK2tbXXURUREJKq7aXmYufsKTt1MgUwqgVJV+uOy+LhPYyeEhnjC1cGyGistnbrPb44ZICIi+o8t5xMQsOIEom+nAkCZQeDfx6NvpyJgxQlsOZ+g9Ro1id0ERERE//JlVByWHb5RqXOVKgFKlYDpu64gJacA4/w8NFyddrBlgIiI6B9bzidUOgj817LDN7BVT1oI2DJARESEJ2ME5u6JLfV4Udp9ZJzajIJ7f0H1OAcy25qwatEFtl4hkJqYP/ecOXti4d3ISWfGEJSGYUCHGeoUFiIiXTRz9xUoShkboMh6hIffT4TEzAo2L/WC1MIGBfevIfN0BAof3oRz/9nPP08lYObuKwgf5aXN0quMTxYdYwxTWIiIdE1cUjZO3Uwp9Xjun1FQFeSizvDPYFrTHQBg07obIKiQ++cxKPNzIDO3fuY8pUrAqZspuJmcjcbOuvuZzTCgI9SZwiIAiE/LQ3hMPDaeuaNzU1iIiPRVRExCmdMHVYV5AACZVY2nXpdZOwASKSTS0h+nMqkEm88mYF6flhqrV9M4gFAHGNsUFiIiXRN1PbnMz15zN08AQOr+VShMug1F1iPkXj2J7Ev7YdO2N6Smzx8zADz5zI66kazxmjWJLQMiM8YpLEREuiSnQIGEtLwy32PRsC3sfIYj68x2PLgZU/K6rfcg2PuOKPceCal5yC1Q6Oy4L92sykhoegpLTWszDGrvppHrEREZi/jUXJS7FC8AuV0tmLm2hGVTb8gsbJF36zyyordBZlUDtm17l3muAOBOai5authppGZNYxgQSXlTWACg4OFNZJ7+AQX3/oKgKIK8Ri1Yt+4G23Z9nvt+fZnCQkSkSwoVqnLfk/vXCaQd/BIuY9ZBbusEALBs6g0IAjKOb4RViy6QWZS9XL869xELxwyIpKwpLADw+O+LeBg+Gcq8TNh5D4Z9wGhYNH4ZyuzSR7sWT2EhIiL1mcrLfxRmX9wP01oNS4JAMcvGL0MoKkBh0m2N3EcsbBkQQXlTWFQFeUjZtxwWjdqjZsgMSCTq/QPSlyksRES6pL6jFSRAmV0FyrwMSJ8zdVBQKZ/8j+L/lkLyz310le7GFANWPIWlNLl/HYcqNwP2vq9DIpFCVZgPQVCveal4CgsREanHykwOt3K6V03sXVCYdAtFafefej33rxOARAqTmvXLPN/N0VJnBw8CbBkQRXlTWPLvXIbEzBKKnFQk7/oEirT7kJiYw+oFPzh0HQ2J3LTUc4unsMyD7s5nJSLSJdeuXYM06SoEWT1IpLLnvsfW6zU8vv0bHm6eBpu2PZ8MILx5Dvm3f4P1i0GQ2ziWen2ZVAK/Js7aKl8j2DJQzdSZwlKUlgiolHi0cyEsGryEmiEzYd0qEDmXDiDll5Xl3qN4CgsRET1fUVERtm/fDn9/fzRv3hx/7fm61CAAAOZuL6D2iKUwrd0IORf3Iy1yPRQZD1HD93U4BL9f5r2UKgHDO+j2TC+2DFQzdaawCEX5EIoKYN2mOxwC3wHwZNSqoCxCzuWDKPIZBhOHuqWfD92ewkJEJJa7d+9i/fr1WL9+PR4+fAgfHx/88MMP6NevH97efBnRt1NLbbk1c2mKWgPnV+h+MqkE3g0ddX4cF1sGqpk6U0uKuwGsmnd56nWrFq8AAAruX9PIfYiIjIFKpcLhw4fRt29f1K9fHytXrkS/fv1w5coVnDx5EkOGDIGZmRlCQzwhL2M8V2XIpRKEhnhq9JrawDBQzdSZWiKzftL39Mwa2FZPvumr8nM0ch8iIkOWmpqKZcuWoUmTJggODsb
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAgMAAAGbCAYAAABZBpPkAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjkuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8hTgPZAAAACXBIWXMAAA9hAAAPYQGoP6dpAABMl0lEQVR4nO3deVzUdf4H8Nd3ZmCUUzkN5fDAC1HzzvJAEcUDxS7No8O1YzPTrM0sNbXcNd1VW6tdzbXWLK0UpbyJCfEislSkVNAfDF4goBwzMjAz398fBisCwwBzMq/n49Hj93O+13tc+X5ffL6fQxBFUQQRERE5LIm1CyAiIiLrYhggIiJycAwDREREDo5hgIiIyMExDBARETk4hgEiIiIHxzBARETk4BgGiIiIHBzDABERkYNjGCAiInJwDANEDfTZZ59BEISq/1q0aIGAgACMHj0aH374IUpKSqxdYqN9+eWXWLdunbXLqNe9f//3/zdq1Chrl0dkd2TWLoDIXi1fvhzt27dHRUUFbty4gR9//BHz5s3DP/7xD8THx6Nnz57WLrHBvvzyS5w7dw7z5s2zdikGbd26tcZnP//8M9avX4+oqCgrVERk3xgGiBopOjoa/fr1q/rzW2+9hcTERIwfPx4xMTH4/fff0bJlSytWaF5lZWVwdnaGRGL5Bsbp06fX+OzHH3+EIAiYOnWqxeshsnd8TUBkQiNGjMDixYuRnZ2NL774otq28+fP47HHHoOXlxdatGiBfv36IT4+vto+la8gjh49irlz58LX1xetWrXCCy+8gPLycty+fRszZ85E69at0bp1a/zlL3/B/QuPqlQqLFiwAIGBgZDL5ejSpQvWrFlTY7/7DR8+HHv37kV2dnZVk3tISAiA/z1ot2/fjnfeeQdt27aFi4sLiouLAQApKSkYM2YMPD094eLigmHDhuHYsWM1rnH16lU899xz8Pf3h1wuR1hYGP7zn/809K+5Bo1Gg507d2LYsGFo165dk89H5GjYMkBkYjNmzMCiRYtw6NAhzJ49GwCQnp6Ohx9+GG3btsXChQvh6uqKr7/+GpMmTcLOnTsRGxtb7RyvvPIK2rRpg2XLluHkyZPYuHEjWrVqhePHjyMoKAgrV67Evn37sHr1avTo0QMzZ84EAIiiiJiYGCgUCsyaNQu9e/fGwYMH8cYbb+Dq1atYu3ZtnXW//fbbKCoqwpUrV6r2c3Nzq7bPihUr4OzsjNdffx0ajQbOzs5ITExEdHQ0+vbti6VLl0IikWDLli0YMWIEkpOTMWDAAABAbm4uBg0aBEEQMGfOHPj6+mL//v2YNWsWiouLm/RqYt++fbh9+zamTZvW6HMQOTSRiBpky5YtIgAxNTW1zn08PT3FBx98sOrPI0eOFMPDw8WysrKqz/R6vTh48GAxNDS0xrlHjx4t6vX6qs8feughURAE8cUXX6z6TKvViu3atROHDRtW9dnu3btFAOJ7771XrZ7HHntMFARBzMzMNPjdxo0bJwYHB9f4XKFQiADEDh06iGq1utp3CA0NrVGvWq0W27dvL44aNarqs1mzZokPPPCAmJ+fX+3cU6ZMET09Paudt6EeffRRUS6Xi7du3Wr0OYgcGV8TEJmBm5tb1aiCwsJCJCYm4oknnkBJSQny8/ORn5+PgoICjB49GhkZGbh69Wq142fNmgVBEKr+PHDgQIiiiFmzZlV9JpVK0a9fP1y+fLnqs3379kEqlWLu3LnVzrdgwQKIooj9+/c36Xs9/fTT1fpBnD59GhkZGXjqqadQUFBQ9d1UKhVGjhyJI0eOQK/XQxRF7Ny5ExMmTIAoilX75efnY/To0SgqKsIvv/zSqJqKi4uxd+9ejB07Fq1atWrS9yNyVHxNQGQGpaWl8PPzAwBkZmZCFEUsXrwYixcvrnX/vLw8tG3bturPQUFB1bZ7enoCAAIDA2t8fuvWrao/Z2dnIyAgAO7u7tX269atW9X2pmjfvn21P2dkZAC4GxLqUlRUhIqKCty+fRsbN27Exo0ba90vLy+vUTXt3LkTZWVlfEVA1AQMA0QmduXKFRQVFaFTp04AAL1eDwB4/fXXMXr06FqPqdy3klQqrXW/2j4X6+kYaEr3j46o/G6rV69G7969az3Gzc0NBQUFAO6OAqgrODR2KOa2bdvg6emJ8ePHN+p4ImIYIDK5yjHwlQ/+Dh06AACcnJwQGRlp1msHBwcjISEBJSUl1VoHzp8/X7XdkHtfTRijY8eOAAAPDw+D383X1xfu7u7Q6XQm/Tu4fv06FAoFnnnmGcjlcpOdl8jRsM8AkQklJiZixYoVaN++fVWztZ+fH4YPH45///vfuH79eo1jbt68abLrjx07FjqdDhs2bKj2+dq1ayEIAqKjow0e7+rqiqKiIqOv17dvX3Ts2BFr1qxBaWlpje2V300qleLRRx/Fzp07ce7cuTr3a6jt27dDr9fzFQFRE7FlgKiR9u/fj/Pnz0Or1SI3NxeJiYk4fPgwgoODER8fjxYtWlTt+9FHH+GRRx5BeHg4Zs+ejQ4dOiA3NxcnTpzAlStXcObMGZPUNGHCBERERODtt99GVlYWevXqhUOHDmHPnj2YN29e1W/ydenbty927NiB1157Df3794ebmxsmTJhQ5/4SiQSffvopoqOjERYWhmeffRZt27bF1atXoVAo4OHhge+++w4A8Le//Q0KhQIDBw7E7Nmz0b17dxQWFuKXX35BQkICCgsLG/x9t23bhoCAAAwfPrzBxxLRPaw5lIHIHlUO/6v8z9nZWWzTpo04atQocf369WJxcXGtx126dEmcOXOm2KZNG9HJyUls27atOH78ePHbb7+tce77hy0uXbpUBCDevHmz2udPP/206OrqWu2zkpIScf78+WJAQIDo5OQkhoaGiqtXr6429K8upaWl4lNPPSW2atVKBFA1zLByaOE333xT63G//vqrOHnyZNHb21uUy+VicHCw+MQTT4g//PBDtf1yc3PFl19+WQwMDBSdnJzENm3aiCNHjhQ3btxYb233O3/+vAhAfO211xp8LBFVJ4iiBXsfERERkc1hnwEiIiIHxz4DRGQzbt68CZ1OV+d2Z2dneHl5WbAiIsfA1wREZDNCQkIMTow0bNgw/Pjjj5YriMhBsGWAiGzGtm3bcOfOnTq3t27d2oLVEDkOtgwQERE5OKNaBvR6Pa5duwZ3d/cGz1BGRERE1iGKIkpKShAQEACJpO4xA0aFgWvXrtVYIIWIiIjsQ05ODtq1a1fndqPCQOUc5zk5OfDw8DBNZURERGRWxcXFCAwMrLGS6f2MCgOVrwY8PDwYBoiIiOxMfa/4OekQERGRg2MYICIicnAMA0RERA6OYYCIiMjBMQwQERE5OIYBIiIiB8cwQERE5OAYBoiIiBwcwwAREZGDYxggIiJycAwDREREDo5hgIiIyMExDBARETk4o1YtJCIiMjdRFFFYWIjs7GwolUpcuXIFd+7cQUVFBbZv347Ro0fDx8cHzs7O8Pf3R3BwMIKCghAQEACpVGrt8u0awwAREVlFdnY2EhMTkZiYiFOnTkGpVEKlUlVtd3Z2houLC5ycnHDz5k2kpaXBy8sLGo2m2n5SqRTt2rVDt27dEBERgREjRuDBBx9kQGgAQRRFsb6diouL4enpiaKiInh4eFiiLiIiaoZ+/vlnbNq0CQkJCbh8+TIEQUCfPn0wePBgtG/fHkFBQQgKCkJwcDB8fX0hCEKt5ykuLkZOTg6USiWys7ORnZ2N06dP48iRI1Cr1fD09MTw4cMxdepUTJ48GU5OThb+prbB2Oc3wwAREZlVRUUFdu7ciQ8//BAnTpxAcHAwYmJiMGLECAwbNgytW7c22bXKy8uRmpqKxMREHDhwAMePH0fbtm3x5z//GbNnz4avr6/JrmUPGAaIiMjq9u/fjxdffBFKpRIjRozA3LlzMX78eIs14aelpeHDDz/EF198AVEU8fbbb2PhwoUO01Jg7PObowmIiMjkbt++jeeeew5jx45F165dcfbsWfzwww+YOHGiRd/lh4eHY9OmTbhy5Qpee+01LFu2DAMGDMDp06c
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "class Graph:\n",
    "    def __init__(self, adj_list: dict = {}, name=\"Graph\", directed=False):\n",
    "        self.plt = plt\n",
    "\n",
    "        self.nx = nx\n",
    "        # validation\n",
    "\n",
    "        tmp = []\n",
    "        for i in adj_list:\n",
    "            tmp.extend(adj_list[i])\n",
    "\n",
    "        if not directed and set(tmp) == set(adj_list.keys()):\n",
    "            self.adj_list = adj_list\n",
    "            self.directed = directed\n",
    "            self.name = name\n",
    "        else:\n",
    "            print(\"Error :  It is not a valid graph\")\n",
    "\n",
    "    def __str__(self):\n",
    "        string = \"  \" + self.name + \"\\n\"\n",
    "        for i in self.adj_list.keys():\n",
    "            string += (\n",
    "                str(i) + \" : [\" + \",\".join([str(j) for j in self.adj_list[i]]) + \"]\\n\"\n",
    "            )\n",
    "        return string\n",
    "\n",
    "    def add_node(self, node):\n",
    "        if node not in self.adj_list.keys():\n",
    "            self.adj_list[node] = []\n",
    "        else:\n",
    "            print(f\"Warning :  the node'{node}' already exists\")\n",
    "\n",
    "    def add_edge(self, node1, node2):\n",
    "        graph = self.adj_list\n",
    "        if node1 in graph and node2 in graph:\n",
    "            graph[node1].append(node2)\n",
    "            if not self.directed:\n",
    "                graph[node2].append(node1)\n",
<<<<<<< HEAD
    "    def get_node_set(self):\n",
    "        return list(self.adj_list.keys())\n",
    "    def get_edg_set(self):\n",
=======
    "\n",
    "    def get_nodeSet(self):\n",
    "        return list(self.adj_list.keys())\n",
    "\n",
    "    def get_edgSet(self):\n",
>>>>>>> ffbe3bbd8623bff453d16b942b7cf035c20d808c
    "        edgSet = []\n",
    "        for i in self.adj_list.keys():\n",
    "            for j in self.adj_list[i]:\n",
    "                edgSet.append(tuple([i, j]))\n",
    "        return edgSet\n",
    "\n",
    "    def dfs(self, node):\n",
    "        if node in self.adj_list.keys():\n",
    "            traverse = []\n",
    "            visited = set()\n",
    "            stack = [node]\n",
    "            while stack:\n",
    "                current = stack.pop()\n",
    "                if current not in visited:\n",
    "                    visited.add(current)\n",
    "                    traverse.append(current)\n",
    "                    stack.extend(self.adj_list[current])\n",
    "\n",
    "            return traverse\n",
    "        else:\n",
    "            print(f\"Error :  node'{node}' does not exist in graph\")\n",
    "\n",
    "    def bfs(self, node):\n",
    "        if node in self.adj_list.keys():\n",
    "            traverse = []\n",
    "            visited = set()\n",
    "            queue = [node]\n",
    "            while queue:\n",
    "                current = queue.pop(0)\n",
    "                if current not in visited:\n",
    "                    visited.add(current)\n",
    "                    traverse.append(current)\n",
    "                    queue.extend(self.adj_list[current])\n",
    "            return traverse\n",
    "\n",
    "        else:\n",
    "            print(f\"Error :  node'{node}' does not exist in graph\")\n",
    "\n",
<<<<<<< HEAD
    "    def get_path(self, n1,n2, path=[]):\n",
    "        g= self.adj_list\n",
    "        path +=[n1]\n",
    "        if n2 not in g[n1]:\n",
    "            for i in g[n1]:\n",
    "                if(i not in path):\n",
    "                    path1 = self.get_path(i, n2, path.copy())\n",
    "                    if(path1):\n",
    "                        return path1  \n",
=======
    "    def getPath(self, n1, n2, path=[]):\n",
    "        g = self.adj_list\n",
    "        path += [n1]\n",
    "        if n2 not in g[n1]:\n",
    "            for i in g[n1]:\n",
    "                if i not in path:\n",
    "                    path1 = self.getPath(i, n2, path.copy())\n",
    "                    if path1:\n",
    "                        return path1\n",
>>>>>>> ffbe3bbd8623bff453d16b942b7cf035c20d808c
    "        else:\n",
    "            return path + [n2]\n",
    "\n",
    "    def opt_path(self, path):\n",
    "        g = self.adj_list\n",
    "        l = len(path)\n",
    "        path1 = path.copy()\n",
    "        t = 2\n",
    "        for i in range(l):\n",
    "            for j in range(i + 2, l):\n",
    "                if abs(j - i) > t:\n",
    "                    n1 = path[i]\n",
    "                    n2 = path[j]\n",
<<<<<<< HEAD
    "                    if(n2 in g[n1]):\n",
    "                        path1 = path[:i+1]+path[j:]\n",
    "                        t = abs(j-i)\n",
    "        return path1 \n",
    "    def sortest_path(self,n1,n2):\n",
    "        path = self.get_path(n1,n2)\n",
    "        spath =self.opt_path(path)\n",
=======
    "                    if n2 in g[n1]:\n",
    "                        path1 = path[: i + 1] + path[j:]\n",
    "                        t = abs(j - i)\n",
    "        return path1\n",
    "\n",
    "    def sortestPath(self, n1, n2):\n",
    "        path = self.getPath(n1, n2)\n",
    "        spath = self.opt_path(path)\n",
>>>>>>> ffbe3bbd8623bff453d16b942b7cf035c20d808c
    "        return spath\n",
    "\n",
    "    def display(self):\n",
    "        G = self.nx.Graph()\n",
    "        G.add_nodes_from(self.get_node_set())\n",
    "        G.add_edges_from(self.get_edg_set())\n",
    "        self.nx.draw_networkx(G)\n",
    "        self.plt.title(self.name)\n",
    "        self.plt.show()\n",
<<<<<<< HEAD
    "    def make_tree(self, Root=None):\n",
=======
    "\n",
    "    def makeTree(self, Root=None):\n",
>>>>>>> ffbe3bbd8623bff453d16b942b7cf035c20d808c
    "        temp_ls = dict()\n",
    "        if (Root == None) or (Root not in self.adj_list.keys()):\n",
    "            root = list(self.adj_list.keys())[0]\n",
    "        else:\n",
    "            root = Root\n",
    "        temp_ls[root] = [root]\n",
    "        stack = [root]\n",
    "\n",
    "        def visite(root):\n",
    "            for i in self.adj_list[root]:\n",
    "                if root not in temp_ls:\n",
    "                    temp_ls[root] = list()\n",
    "                if i not in stack:\n",
    "                    stack.append(i)\n",
    "                    temp_ls[root].append(i)\n",
    "                    visite(i)\n",
    "\n",
    "        visite(root)\n",
    "\n",
    "        return temp_ls\n",
    "\n",
    "\n",
    "adj_list = {\n",
    "    0: [3, 5, 9, 10, 1],\n",
    "    1: [6, 7, 4, 0, 10],\n",
    "    2: [10, 5],\n",
    "    3: [0],\n",
    "    4: [1, 5, 8],\n",
    "    5: [2, 0, 4],\n",
    "    6: [1],\n",
    "    7: [1],\n",
    "    8: [4],\n",
    "    9: [0],\n",
    "    10: [2, 0],\n",
    "}\n",
    "g = Graph(adj_list, name=\"Demo\")\n",
    "g.display()\n",
    "for i in adj_list:\n",
<<<<<<< HEAD
    "    \n",
    "    g1 = Graph(g.make_tree(Root=i),name=\"Demo tree_\"+str(i))\n",
    "    g1.display()\n"
=======
    "    g1 = Graph(g.makeTree(Root=i), name=\"Demo tree_\" + str(i))\n",
    "    g1.display()"
>>>>>>> ffbe3bbd8623bff453d16b942b7cf035c20d808c
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "29d9be84",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "03f1967f",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "8db9672a",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "457ca038",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  Demo\n",
      "0 : [3,5,9,10,1]\n",
      "1 : [6,7,4,0,10]\n",
      "2 : [10,5]\n",
      "3 : [0]\n",
      "4 : [1,5,8]\n",
      "5 : [2,0,4]\n",
      "6 : [1]\n",
      "7 : [1]\n",
      "8 : [4]\n",
      "9 : [0]\n",
      "10 : [2,0]\n",
      "\n",
      "  Demo\n",
      "0 : [3,5,9,10,1]\n",
      "1 : [6,7,4,0,10]\n",
      "2 : [10,5]\n",
      "3 : [0]\n",
      "4 : [1,5,8]\n",
      "5 : [2,0,4]\n",
      "6 : [1]\n",
      "7 : [1]\n",
      "8 : [4,10]\n",
      "9 : [0]\n",
      "10 : [2,0,8]\n",
      "\n",
      "[8, 10]\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAgMAAAGbCAYAAABZBpPkAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjkuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8hTgPZAAAACXBIWXMAAA9hAAAPYQGoP6dpAABlNklEQVR4nO3dd1yV5fsH8M8Z7KWAqCi4AAfiyMFQUFJxU2qppdgwyxxpWmY21b72NWdWauX84sxypXbEgYqCSDlCHICm4AAElCnjnPP8/jD4RWw8h+eMz/v18pWeZ9wXiTzXc9/Xfd8SQRAEEBERkdGSih0AERERiYvJABERkZFjMkBERGTkmAwQEREZOSYDRERERo7JABERkZFjMkBERGTkmAwQEREZOSYDRERERo7JABERkZFjMkCkJzZt2gSJRFL6y9zcHM7Ozhg4cCBWrVqFnJwcsUMkIj0lFzsAIqqdBQsWoFWrViguLkZKSgpOnDiBmTNnYvny5di/fz86deokdohEpGck3KiISD9s2rQJr732GmJiYtC9e/cyx44fP45hw4bByckJV69ehYWFhUhREpE+4jABkQF49tln8cknn+D27dvYsmVL6efXrl3DCy+8AHt7e5ibm6N79+7Yv39/mWtLhh9Onz6Nd955B40aNUKDBg3w1ltvoaioCI8ePcKECRPQsGFDNGzYEHPmzMG/3yHy8vIwe/ZsuLi4wMzMDG3btsXSpUvLnUdEuonJAJGBCAkJAQCEhYUBAOLi4uDj44OrV69i7ty5WLZsGaysrPD8889jz5495a6fPn06EhISMH/+fAQHB+OHH37AJ598guHDh0OlUmHRokXo3bs3lixZgtDQ0NLrBEFAcHAwVqxYgUGDBmH58uVo27Yt3n//fcyaNat+vngiejoCEemFjRs3CgCEmJiYSs+xs7MTunbtKgiCIPTr10/w8vISCgoKSo+r1WrBz89PcHd3L3ffgQMHCmq1uvRzX19fQSKRCJMnTy79TKlUCs2bNxf69OlT+tnevXsFAMIXX3xRJpYXXnhBkEgkQmJiYp2/ZiKqH+wZIDIg1tbWyMnJQWZmJo4fP47Ro0cjJycH6enpSE9PR0ZGBgYOHIiEhATcvXu3zLUTJ06ERCIp/bO3tzcEQcDEiRNLP5PJZOjevTtu3rxZ+tmhQ4cgk8nwzjvvlLnf7NmzIQgCfvvtNy19tUSkKZxNQGRAcnNz4eTkhMTERAiCgE8++QSffPJJheempaWhWbNmpX92dXUtc9zOzg4A4OLiUu7zhw8flv759u3bcHZ2ho2NTZnz2rdvX3qciHQbkwEiA3Hnzh1kZWXBzc0NarUaAPDee+9h4MCBFZ7v5uZW5s8ymazC8yr6XGBhIJFBYTJAZCBKivoGDhyI1q1bAwBMTEzQv39/rbbbokULHD16FDk5OWV6B65du1Z6nIh0G2sGiAzA8ePHsXDhQrRq1Qrjxo2Dk5MT+vbti++//x73798vd/6DBw801vaQIUOgUqnw7bfflvl8xYoVkEgkGDx4sMbaIiLtYM8AkZ757bffcO3aNSiVSqSmpuL48eM4cuQIWrRogf3798Pc3BwA8N1336F3797w8vLCpEmT0Lp1a6SmpiIqKgp37tzBpUuXNBLP8OHDERgYiI8++gi3bt1C586dERYWhn379mHmzJlo06aNRtohIu1hMkCkZz799FMAgKmpKezt7eHl5YWVK1fitddeK9NN36FDB/z++++YP38+Nm3ahIyMDDg5OaFr166l99AEqVSK/fv349NPP8XOnTuxceNGtGzZEkuWLMHs2bM11g4RaQ+XIyYiIjJyrBkgIiIyckwGiIiIjByTASIiIiPHZICIiMjIMRkgIiIycjWaWqhWq3Hv3j3Y2NiU2ciEiIiIdJcgCMjJyYGzszOk0srf/2uUDNy7d6/cZiVERESkH5KTk9G8efNKj9coGShZyCQ5ORm2traaiYyIiIi0Kjs7Gy4uLuV2Ff23GiUDJUMDtra2TAaIiIj0THVD/CwgJCIiMnJMBoiIiIwckwEiIiIjx2SAiIjIyDEZICIiMnJMBoiIiIwckwEiIiIjx2SAiIjIyDEZICIiMnJMBoiIiIwckwEiIiIjx2SAiIjIyDEZICIiMnJMBoiIiIwckwEiIiIjx2SAiIjIyMnFDoCIjEteoRK3MvJQpFTDVC5FSwcrWJnxRxGRmPgvkIi0LiE1B1ujkxB+PQ1JmfkQ/nFMAsDV3hKBbZ0wztsV7o1txAqTyGhJBEEQqjspOzsbdnZ2yMrKgq2tbX3ERUQGIDkzH/P2xCIiMR0yqQQqdeU/bkqO+7s5YtEIL7jYW9ZjpESGqabPb9YMEJFW7IhJQv8VJxF5MwMAqkwE/nk88mYG+q84iR0xSVqPkYie4DABEWnct+EJWBoWX6drVWoBKrWAubtjkZ5biGmB7hqOjoj+jT0DRKRRO2KS6pwI/NvSsHjsZA8BkdaxZ4CINCY5Mx+f7Y+r8FjRg9vIOr0NRSmJUOU9gsTEDCYOLrD1HglLd+9K7/np/jj4tXFkDQGRFrFngIg0Zt6eWCgrqQ1QZadBXfQYVl790LD/JNj5jQEAPPhlIXIuKiq9p1ItYN6eWK3ES0RPsGeAiDQiITUHEYnplR63aNMDFm16lPnMptsw3N80E9nn9sKmy6AKr1OpBUQkpiMxLQduTpx2SKQN7BkgIo3YGp0EmVRSq2skUhnkNo5QF+ZWeZ5MKsGWs6wdINIWJgNEpBHh19OqnT4IAOqiAqjys1D88D6yz+3F45t/wLxF5yqvUakFhMenaSpUIvoXDhMQ0VPLLVQiKTO/Ruc+PL4OuSU1AhIpLD18YR/0drXXJWXkI69QyaWLibSA/6qI6KndzshD9X0CT9j2eA6W7XpDlZOB/GunIQhqQFVc7XUCgFsZefB0tnuqWImoPA4TENFTK1Kqa3yuiYMLLFp2gbVXPzi9+BmEogKk/bwANVgZvVbtEFHNMRkgoqdmKq/7jxLLdr1QdD8Bysy7Wm2HiCrHf1lE9NRaOlihdvMI/p9QXAgAUBfmVXme5O92iEjzmAwQ0VOzMpPDtZoVAlV5j8p9JqiUyLt8HBK5GUwcXau83tXBksWDRFrCf1lEpBGBbZ0QGn270umFGYpvIRTlw8ylI2Q2DlDlPkTelRNQZtxBw2cnQmpqUem9ZVIJAj2ctBU6kdFjMkBEGjHO2xWbom5VetyqvT9y/zyCnAuHoH6cA6mpBUybuKFh39eq3JsAeLLOwHifqnsOiKjumAwQkUa4N7aBv5sjIm9mVNg7YNWhD6w69Kn1fWVSCfxaO3ApYiItYs0AEWnMohFekNdySeLqyKUSLBrhpdF7ElFZTAaISGNc7C0xP9hTo/dcEOzJ7YuJtIzJABFp1NgerngvyEMj93o/qC3G9GCtAJG2sWaAiDRuWqA7HK3N8Nn+OCjVQo02MCohk0ogl0qwINiTiQBRPWHPABFpxdgerjj6bh/4tXYAAEir2b2gZPtjv9YOOPpuHyYCRPWIPQNEpDUu9pYIneiNhNQchMz/AQ9MGkFt6VAmLZDgyYJCgR5OGO/jylkDRCJgMkCiyytU4lZGHoqUapjKpWjpYMWV5gxMa0dLxO/4D6ZPn445817m3zeRjuG/QBJFQmoOtkYnIfx6GpIy88u/KdpbIrCtE8Z5u8K9Md8U9V1MTAwePnyIQYMGwcpMzm2IiXQMkwGqV8mZ+Zi3JxYRiemQSSUVFpYJAG5n5iM0+jY2Rd2Cv5sjFo3w4vQyPaZQKNCwYUP06NFD7FCIqAIsIKR6syMmCf1XnETkzQwAqLbCvOR45M0M9F9xEjtikrQeI2mHQqHAgAEDIJfz/YNIFzEZoHrxbXgC5u6ORaFSXatpZsCTpKBQqcbc3bH4NjxBSxGStmRkZODcuXMYNGiQ2KEQUSWYDJDW7YhJwtKweI3ca2lYPHayh0CvHDlyBIIgYODAgWKHQkSVYJ8daVVyZj4+2x9X6fHClEQ8Ovk/FN69CgAwc26HhoGvwbRx60qv+XR/HPzaOLKGQE8oFAp4eXnB2dlZ7FCIqBL
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "print(g)\n",
    "g.add_edge(8, 10)\n",
    "print(g)\n",
<<<<<<< HEAD
    "print(g.sortest_path(8,10))\n",
=======
    "print(g.sortestPath(8, 10))\n",
>>>>>>> ffbe3bbd8623bff453d16b942b7cf035c20d808c
    "g.display()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "affba892",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "9862c226",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1, 2, 2, 3, 4, 5, 1, 7, 9, 90, 23, 41]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "class Tree:\n",
    "    def __init__(self, data, parent=None):\n",
    "        self.data = data\n",
    "        self.childs = []\n",
    "\n",
    "    def addChild(self, *nodes):\n",
    "        childs = [Tree(i, parent=self) for i in nodes]\n",
    "        self.childs.extend(childs)\n",
    "        if len(childs) == 1:\n",
    "            return childs[0]\n",
    "        return childs\n",
<<<<<<< HEAD
    "    \n",
    "    def get_childs(self):\n",
    "            return [i.data for i in self.childs]\n",
=======
    "\n",
    "    def getChilds(self):\n",
    "        return [i.data for i in self.childs]\n",
    "\n",
>>>>>>> ffbe3bbd8623bff453d16b942b7cf035c20d808c
    "    def getElements(self):\n",
    "        elements = [self.data]\n",
    "        for i in self.childs:\n",
    "            elements.extend(i.getElements())\n",
    "        return elements\n",
    "\n",
    "    def traverse(self, order=\"pre\"):\n",
    "        ls = []\n",
    "        if order == \"pre\":\n",
    "            ls.append(self.data)\n",
    "            for i in self.childs:\n",
    "                ls.extend(i.traverse(order=order))\n",
    "            return ls\n",
    "        elif order == \"post\":\n",
    "            for i in self.childs:\n",
    "                ls.extend(i.traverse(order=order))\n",
    "            ls.append(self.data)\n",
    "            return ls\n",
    "\n",
    "\n",
    "tree = Tree(1)\n",
    "t2 = tree.addChild(2)\n",
    "t2t3 = t2.addChild(2, 3, 4, 5, 1, 7, 9)\n",
    "tree.addChild(90, 23, 41)\n",
    "tree.getElements()\n",
    "# tree.traverse()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "102b3cb1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[2, 3, 4, 5, 1, 7, 9, 2, 90, 23, 41, 1]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tree.traverse(\"post\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "69202f88",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "99b975a8",
   "metadata": {},
   "outputs": [],
   "source": [
    "class BTree:\n",
    "    def __init__(self, data, parent=None):\n",
    "        self.data = data\n",
    "        self.left = None\n",
    "        self.right = None\n",
    "        self.parent = parent\n",
    "\n",
    "    def getElement(self, idx):\n",
    "        path = []\n",
    "        while idx > 0:\n",
    "            if idx % 2 == 1:\n",
    "                path.append((idx % 2))\n",
    "                idx //= 2\n",
    "            else:\n",
    "                path.append((idx % 2) + 2)\n",
    "                idx = idx // 2 - 1\n",
    "        temp = self\n",
    "        while path and temp:\n",
    "            dr = path.pop()\n",
    "            if dr == 1:\n",
    "                temp = temp.left\n",
    "            else:\n",
    "                temp = temp.right\n",
    "        if temp:\n",
    "            return temp\n",
    "        else:\n",
    "            print(\"id does not exists\")\n",
<<<<<<< HEAD
    "                \n",
    "    def get_depth(self):\n",
    "        ld = self.left.get_depth() if self.left else -1\n",
    "        rd = self.right.get_depth() if self.right else -1\n",
    "        return max(ld,rd)+1\n",
    "    def is_balanced(self):\n",
    "        ld = self.left.get_depth() if self.left else -1\n",
    "        rd= self.right.get_depth() if self.right else -1\n",
    "        if(abs(ld-rd) in [0,1]):\n",
    "            lb = self.left.is_balanced() if self.left else True\n",
    "            rb = self.right.is_balanced() if self.right else True\n",
    "            return bool(lb*rb)\n",
    "        \n",
    "    def get_parent(self):\n",
    "        return self.parent\n",
    "    \n",
    "    def get_childs(self):\n",
    "        return [self.left, self.right]\n",
    "    \n",
    "    def get_id(self):\n",
    "        if(self.parent != None):\n",
    "            if(self == self.parent.left):\n",
    "                return self.parent.get_id()*2 + 1\n",
    "            else:\n",
    "                return self.parent.get_id()*2 + 2\n",
=======
    "\n",
    "    def getDepth(self):\n",
    "        ld = self.left.getDepth() if self.left else -1\n",
    "        rd = self.right.getDepth() if self.right else -1\n",
    "        return max(ld, rd) + 1\n",
    "\n",
    "    def isBalanced(self):\n",
    "        ld = self.left.getDepth() if self.left else -1\n",
    "        rd = self.right.getDepth() if self.right else -1\n",
    "        if abs(ld - rd) in [0, 1]:\n",
    "            lb = self.left.isBalanced() if self.left else True\n",
    "            rb = self.right.isBalanced() if self.right else True\n",
    "            return bool(lb * rb)\n",
    "\n",
    "    def getParent(self):\n",
    "        return self.parent\n",
    "\n",
    "    def getChilds(self):\n",
    "        return [self.left, self.right]\n",
    "\n",
    "    def getId(self):\n",
    "        if self.parent != None:\n",
    "            if self == self.parent.left:\n",
    "                return self.parent.getId() * 2 + 1\n",
    "            else:\n",
    "                return self.parent.getId() * 2 + 2\n",
>>>>>>> ffbe3bbd8623bff453d16b942b7cf035c20d808c
    "        else:\n",
    "            return 0\n",
    "\n",
    "    def __setattr__(self, key, value):\n",
    "        self.__dict__[key] = value\n",
    "        if value:\n",
    "            if key in [\"left\", \"right\"]:\n",
    "                value.parent = self\n",
<<<<<<< HEAD
    "            \n",
    "            \n",
    "    def get_size(self):\n",
    "        lsize = self.left.get_size() if self.left else 0\n",
    "        rsize = self.right.get_size() if self.right else 0\n",
    "        return lsize+1+rsize\n",
    "    \n",
    "    def add_data(self, data, idx=-1):\n",
    "        if(idx==-1):\n",
    "            q = [] \n",
    "            q.append(self) \n",
    "            while (len(q)): \n",
    "                temp = q[0] \n",
    "                q.pop(0) \n",
    "                if (not temp.left):\n",
    "                    temp.left = BTree(data, parent=temp) \n",
=======
    "\n",
    "    def getSize(self):\n",
    "        lsize = self.left.getSize() if self.left else 0\n",
    "        rsize = self.right.getSize() if self.right else 0\n",
    "        return lsize + 1 + rsize\n",
    "\n",
    "    def addData(self, data, idx=-1):\n",
    "        if idx == -1:\n",
    "            q = []\n",
    "            q.append(self)\n",
    "            while len(q):\n",
    "                temp = q[0]\n",
    "                q.pop(0)\n",
    "                if not temp.left:\n",
    "                    temp.left = BTree(data, parent=temp)\n",
>>>>>>> ffbe3bbd8623bff453d16b942b7cf035c20d808c
    "                    break\n",
    "                else:\n",
    "                    q.append(temp.left)\n",
    "                if not temp.right:\n",
    "                    temp.right = BTree(data, parent=temp)\n",
    "                    break\n",
    "                else:\n",
    "                    q.append(temp.right)\n",
    "        else:\n",
    "            dr = idx % 2\n",
    "            if dr == 1:\n",
    "                ele = self.getElement(idx // 2)\n",
    "                ele.left = BTree(data, parent=ele)\n",
    "            else:\n",
    "                ele = self.getElement(idx // 2 - 1)\n",
    "                ele.right = BTree(data, parent=ele)\n",
<<<<<<< HEAD
    "    def add_node(self, node, idx=-1):\n",
    "        if(idx==-1):\n",
    "            q = [] \n",
    "            q.append(self) \n",
    "            while (len(q)): \n",
    "                temp = q[0] \n",
    "                q.pop(0) \n",
    "                if (not temp.left):\n",
    "                    temp.left = node \n",
=======
    "\n",
    "    def addNode(self, node, idx=-1):\n",
    "        if idx == -1:\n",
    "            q = []\n",
    "            q.append(self)\n",
    "            while len(q):\n",
    "                temp = q[0]\n",
    "                q.pop(0)\n",
    "                if not temp.left:\n",
    "                    temp.left = node\n",
>>>>>>> ffbe3bbd8623bff453d16b942b7cf035c20d808c
    "                    break\n",
    "                else:\n",
    "                    q.append(temp.left)\n",
    "                if not temp.right:\n",
    "                    temp.right = node\n",
    "                    break\n",
    "                else:\n",
    "                    q.append(temp.right)\n",
    "\n",
    "    def traverse(self, order=\"pre\"):\n",
    "        ls = []\n",
    "        if order == \"pre\":\n",
    "            ls.append(self.data)\n",
    "            if self.left:\n",
    "                ls.extend(self.left.traverse(order))\n",
    "            if self.right:\n",
    "                ls.extend(self.right.traverse(order))\n",
    "            return ls\n",
    "        elif order == \"post\":\n",
    "            if self.left:\n",
    "                ls.extend(self.left.traverse(order))\n",
    "            if self.right:\n",
    "                ls.extend(self.right.traverse(order))\n",
    "            ls.append(self.data)\n",
    "            return ls\n",
    "        elif order == \"in\":\n",
    "            if self.left:\n",
    "                ls.extend(self.left.traverse(order))\n",
    "            ls.append(self.data)\n",
    "            if self.right:\n",
    "                ls.extend(self.right.traverse(order))\n",
    "            return ls"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "9a28bb90",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[3, 4, 1, 5, 2, 0]"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bt = BTree(0)\n",
    "bt.left = BTree(1)\n",
    "bt.right = BTree(2)\n",
    "bt.left.left = BTree(3)\n",
    "bt.left.right = BTree(4)\n",
    "bt.right.left = BTree(5)\n",
    "\n",
    "\n",
    "# bt.getElement(5)\n",
    "bt.traverse(\"post\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "af6dc0c6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[9, 8, 17, 5, 11, 3, 4, 6, 14]"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "btr = BTree(3)\n",
    "ls = [5, 6, 8, 11, 4, 14, 9, 17]\n",
    "for i in ls:\n",
    "    btr.add_data(i)\n",
    "btr.traverse(order=\"in\")\n",
    "# btr.getElement(5).get_id()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "d77046ab",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[3, 50, 6, 4, 14]"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "btr.add_data(50, idx=1)\n",
    "btr.traverse()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "aa1c5c64",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "btr.data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "26662a5c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(6, 5)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "btr.getElement(1).get_id()\n",
    "\n",
    "\n",
<<<<<<< HEAD
    "bt.get_size(),btr.get_size()"
=======
    "bt.getSize(), btr.getSize()"
>>>>>>> ffbe3bbd8623bff453d16b942b7cf035c20d808c
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "83acc37e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[3, 50, 6, 4, 14]"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "btr.traverse()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "563a1e0c",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "3d20a2c3-fbfb-454e-83fc-95f70d674426",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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